Answer:
All the trigonometric ratios are mentioned and the value of x = 51.32°
Step-by-step explanation:
we are given the value of cosx = [tex]\frac{5}{8}[/tex]
We have to find all the other 5 trigonometric values.
sinx = [tex]\sqrt{1-cos^{2}x }[/tex] = [tex]\sqrt{1-(\frac{5}{8})^{2} }[/tex]
= [tex]\sqrt{\frac{39}{64}} = \frac{\sqrt{39}}{8}[/tex]
tanx = [tex]\frac{sinx}{cosx}[/tex] = [tex]\frac{\sqrt{39} }{5}[/tex]
cosecx = [tex]\frac{8}{\sqrt{39} }[/tex]
secx = [tex]\frac{8}{5}[/tex]
cotx = [tex]\frac{1}{tanx}[/tex] = [tex]\frac{5}{\sqrt{39} }[/tex]
These are the values of the trigonometric functions.
cosx = [tex]\frac{5}{8}[/tex]
x = [tex]cos^{-1} \frac{5}{8}[/tex]
x = 51.32°
The other acute angle = 90 - 51.32 = 38.68°
